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(Usually one-parameter) semigroups of linear operators and their applications to partial differential equations, stochastic processes such as Markov processes and other branches of mathematics.

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Smoothing properties of analytic semigroups

Assume $A$ is a second order operator, generator of a positive analytic semigroup on the $L^p$-spaces with $p\in (1,\infty)$ and domain $D(A_p)=W^{2,p}$. Do we have regularity estimates $\|T_p(t)f\|_ …